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course mth158
july 4
007. `* 7
* R.7.10 (was R.7.6). Show how you reduced (x^2 + 4 x + 4) / (x^4 - 16) to lowest terms.
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Your solution:
First you need to factor (x^2 + 4 x + 4) / (x^4 - 16) =(x+2) (x+2)/(x^2-4)(x^2-4)
Now (x^2-4)(x^2-4) can be factored further so this = (x+2) (x-2) (x+2)(x-2)
The factored problem looks like =(x+2) (x+2)/ (x+2) (x-2) (x+2)(x-2)
The numerator cancels out with 2 terms from the denominator and so the final answer = 1/(x-2)^2
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